derivative of log10 x

Question

log₁₀

Answer 1

Suppose we have log_a (b), we want to change it on exponential (e) base, then it can be written as:

log_a(b)=log_a(e)⋅log_e(b)

Let's say we have, y = c ⋅ f ( x ) , where c is a constant then, y ' = c ⋅ f ' ( x )

Now, this is quite straightforward to differentiate, as log₁₀(e) is constant, so only remaining function is log_e(x)

Hence,

y' = log₁₀(e) . 1/x